Farm that Q
Veigar blows things up. He nukes invincible champions and laughs at them. Always remember that this is his purpose.
Start the game by farming Q. Ignore your enemy for the first 5 levels. Just focus on getting your Q farmed. Don't waste a single shot that can kill a minion. It doesn't matter if he's beating the **** out of you, just play defensive and farm that Q.
After 6, change gears and kill him once or twice by nuking him with your R. Keep farming Q. Through the whole game, this is your major advantage. 1 AP at a time, 2 AP at a time, just keep building it.
If you are walking across the map to join a fight, kill a little minion with q on your way while you do it. It slows you such a small amount that it probably won't matter to the fight at hand. If you can manage to kill champs with Q, even better.